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The easiest derivation of rod's moment of inertia? 
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#1
Jan2013, 09:52 AM

P: 27

1. The problem statement, all variables and given/known data
Derive the formula for rod's moment of inertia: I = ml^{2}/12 2. Relevant equations I = ml^{2}/12 3. The attempt at a solution The only one derivation I know of is dividing the rod into two parts and then integrating from 0 to l/2. However' I'd love to know if there's some easier (or more "natural"?) way to do it? Or, if not, maybe you know some website where it's explained as if I were five so that I can get the grasp of it? Because looking at bare integrals, I don't quite know what I'm calculating. 


#2
Jan2013, 10:14 AM

HW Helper
P: 6,202

I think the easiest way would be to just do the integral.
I= ∫ r^{2} dm If you consider a small infinitesimal piece at a distance 'dr' from the center of mass of the rod, the mass of this piece will be dm. Then you just use the fact that mass = mass per unit length * distance i.e. dm = M/L * dr 


#3
Jan2013, 11:06 AM

P: 27

I see. Thanks :)



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